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Symmetry
Volume 17
Issue 5
10.3390/sym17050644
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Article

Characterization of Degree Energies and Bounds in Spectral Fuzzy Graphs

by
Ruiqi Cai
1,†,‡,
Buvaneswari Rangasamy
2,†,
Senbaga Priya Karuppusamy
2,*,† and
Aysha Khan
3
1
Department of Computer Science, Software Engineering Institute of Guangzhou, Guangzhou 510006, China
2
Department of Mathematics, Sri Krishna Arts and Science College, Coimbatore 641008, India
3
Department of Mathematics, University of Technology and Applied Sciences, Musanna 314, Oman
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
‡
Current address: Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510000, China.
Symmetry 2025, 17(5), 644; https://doi.org/10.3390/sym17050644
Submission received: 3 March 2025 / Revised: 17 April 2025 / Accepted: 21 April 2025 / Published: 25 April 2025
(This article belongs to the Special Issue Research on Fuzzy Logic and Mathematics with Applications, 3rd Edition)
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Abstract

This study explores the degree energy of fuzzy graphs to establish fundamental spectral bounds and characterize adjacency structures. We derive upper bounds on the sum of squared degree eigenvalues based on vertex degree distributions and formulate constraints using the characteristic polynomial of the maximum degree matrix. Furthermore, we demonstrate that the average degree energy of a connected fuzzy graph remains strictly positive. The proposed framework is applied to protein–protein interaction networks, identifying critical proteins and enhancing network resilience analysis.
Keywords: fuzzy graph energy; eigenvalues; spectral graph theory; energy bounds; degree matrix; degree energy; maximum degree energy; minimum degree energy fuzzy graph energy; eigenvalues; spectral graph theory; energy bounds; degree matrix; degree energy; maximum degree energy; minimum degree energy

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MDPI and ACS Style

Cai, R.; Rangasamy, B.; Karuppusamy, S.P.; Khan, A. Characterization of Degree Energies and Bounds in Spectral Fuzzy Graphs. Symmetry 2025, 17, 644. https://doi.org/10.3390/sym17050644

AMA Style

Cai R, Rangasamy B, Karuppusamy SP, Khan A. Characterization of Degree Energies and Bounds in Spectral Fuzzy Graphs. Symmetry. 2025; 17(5):644. https://doi.org/10.3390/sym17050644

Chicago/Turabian Style

Cai, Ruiqi, Buvaneswari Rangasamy, Senbaga Priya Karuppusamy, and Aysha Khan. 2025. "Characterization of Degree Energies and Bounds in Spectral Fuzzy Graphs" Symmetry 17, no. 5: 644. https://doi.org/10.3390/sym17050644

APA Style

Cai, R., Rangasamy, B., Karuppusamy, S. P., & Khan, A. (2025). Characterization of Degree Energies and Bounds in Spectral Fuzzy Graphs. Symmetry, 17(5), 644. https://doi.org/10.3390/sym17050644

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